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Minimum polarizability principle of spin states

In a recently published paper in Journal of Computational Methods in Sciences and Engineering, we have been investigating if the MPP (minimum polarizability principle) holds for spin states. I.e. if the most stable spin state has the lowest polarizability value. Intuitively, one might expect such a relationship to hold, since the more strongly bound are electrons, the more difficult it is to let them move (i.e. polarize); also, the more strongly bound are electrons, the more stable should be the molecule.

However, this turns out to correct only in certain cases. Several examples are presented where the low spin state is more stable, but has a higher polarizability than the high spin state; and reversely.